If a triangle has sides a, b, c and r_1 r_2 | vedclass

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(A) The ex-radii are given by $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$,where $\Delta$ is the area and $s$

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$a > b > c$

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(A) The ex-radii are given by $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$,where $\Delta$ is the area and $s$ is the semi-perimeter.Given $r_1 > r_2 > r_3$,we have:$\frac{\Delta}{s-a} > \frac{\Delta}{s-b} > \frac{\Delta}{s-c}$Since $\Delta > 0$,taking the reciprocal reverses the inequality:$s-a Subtracting $s$ from all parts:$-a Multiplying by $-1$ reverses the inequality again:$a > b > c$

If a triangle has sides $a, b, c$ and $r_1 > r_2 > r_3$ (where $r_1, r_2, r_3$ are the ex-radii),then:

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